2017

## Julija Zavadlav, Rudolf Podgornik, Matej PraprotnikOrder and interactions in DNA arrays: Multiscale molecular dynamics simulation Sci. Rep. 7, 4775, 2017.

Abstract
While densely packed DNA arrays are known to exhibit hexagonal and orthorhombic local packings, the detailed mechanism governing the associated phase transition remains rather elusive. Furthermore, at high densities the atomistic resolution is paramount to properly account for fine details, encompassing the DNA molecular order, the contingent ordering of counterions and the induced molecular ordering of the bathing solvent, bringing together electrostatic, steric, thermal and direct hydrogen-bonding interactions, resulting in the observed osmotic equation of state. We perform a multiscale simulation of dense DNA arrays by enclosing a set of 16 atomistically resolved DNA molecules within a semi-permeable membrane, allowing the passage of water and salt ions, and thus mimicking the behavior of DNA arrays subjected to external osmotic stress in a bathing solution of monovalent salt and multivalent counterions. By varying the DNA density, local packing symmetry, and counterion type, we obtain osmotic equation of state together with the hexagonal-orthorhombic phase transition, and full structural characterization of the DNA subphase in terms of its positional and angular orientational fluctuations, counterion distributions, and the solvent local dielectric response profile with its order parameters that allow us to identify the hydration force as the primary interaction mechanism at high DNA densities.

## Luigi Delle Site, Matej PraprotnikMolecular systems with open boundaries: Theory and simulation Phys. Rep., 2017.

Abstract
Typical experimental setups for molecular systems must deal with a certain coupling to the external environment, that is, the system is open and exchanges mass, momentum, and energy with its surroundings. Instead, standard molecular simulations are mostly performed using periodic boundary conditions with a constant number of molecules. In this review, we summarize major development of simulation methodologies, which, contrary to standard techniques, open up the boundaries of a molecular system and allow for exchange of energy and matter with the environment, in and out of equilibrium. In particular, we construct the review around the open boundary simulation approaches based on the Adaptive Resolution Scheme (AdResS), which seamlessly couples different levels of resolution in molecular simulations. Ideas and theoretical concepts used in its development lie at the crossroad of different fields and disciplines and open many different directions for future developments in molecular simulation. We examine progress related to theoretical as well as novel modeling approaches bridging length scales from quantum to the continuum description and report on their application in various molecular systems. The outlook of the review is dedicated to the perspective of how to further incorporate rigorous theoretical approaches such as the Bergmann–Lebowitz and Emch–Sewell models into the molecular simulation algorithms and stimulate further development of open boundary simulation methods and their application.

## Jurij Sablic, Matej Praprotnik, Rafael Delgado-BuscalioniDeciphering the dynamics of star molecules in shear flow Soft Matter 13, 4971-4987. 2017.

Abstract
This work analyses the rotation of star polymers under shear flow, in melts, and in good solvent dilute solution. The latter is modeled by single molecule Brownian hydrodynamics, while melts are modeled using non-equilibrium molecular dynamics in closed (periodic) boxes and in open boundaries. A Dissipative-Particle-Dynamics (DPD) thermostat introduces pairwise monomer friction in melts at will, in directions normal and tangent to the monomer-monomer vectors. Although tangent friction is seldom modeled, we show it is essential to control hydrodynamic effects in melts. We analyze the different sources of molecular angular momentum in solution and melts and distinguish three dynamic regimes as the shear rate $\dot{\gamma}$ is increased. These dynamic regimes are related with the disruption of the different relaxation mechanism of the star in equilibrium. Although, strong differences are found between harmonic springs and finitely extensible bonds, above a critical shear rate the star molecule performs a breathing'' mode with successive elongations and contractions in flow direction with frequency $\Omega$. The force balance in flow direction unveils a relation between $\Omega$ and the orientation angle. Using literature results for the tumbling of rings and linear chains, either in melt or solution, we show that the relation is general. A different tank-treading'' dynamics determines the rotation of monomers around the molecule center of mass. We show that the tank-treading frequency does not saturate but keeps increasing with $\dot{\gamma}$. This is at odds with previous studies which erroneously calculated the molecular angular frequency, used as a proxy to tank-treading.

2016

## Julija Zavadlav, Siewert J. Marrink, Matej PraprotnikAdaptive resolution simulation of supramolecular water: The concurrent making, breaking, and remaking of water bundles J. Chem. Theory Comput. 12, 4138-4145, 2016.

Abstract
The adaptive resolution scheme (AdResS) is a multiscale molecular dynamics simulation approach that can concurrently couple atomistic (AT) and coarse-grained (CG) resolution regions, i.e., the molecules can freely adapt their resolution according to their current position in the system. Coupling to supramolecular CG models, where several molecules are represented as a single CG bead, is challenging but it provides higher computational gains and connection to the established MARTINI CG force field. Difficulties that arise from such coupling have been so far bypassed with bundled AT water models, where additional harmonic bonds between oxygen atoms within a given supramolecular water bundle are introduced. While these models simplify the supramolecular coupling, they also cause in certain situations spurious artifacts, such as partial unfolding of biomolecules. In this work, we present a new clustering algorithm SWINGER that can concurrently make, break and remake water bundles and in conjunction with the AdResS permits the use of original AT water models. We apply our approach to simulate a hybrid SPC/MARTINI water system and show that the essential properties of water are correctly reproduced with respect to the standard monoscale simulations. The developed hybrid water model can be used in biomolecular simulations, where a significant speed up can be obtained without compromising the accuracy of the AT water model.

## Julija Zavadlav, Rudolf Podgornik, Manuel N. Melo, Siewert J. Marrink, Matej PraprotnikAdaptive resolution simulation of an atomistic DNA molecule in MARTINI salt solution Eur. Phys. J. Special Topics 225, 1595-1607, 2016.

Abstract
We present a dual-resolution model of a deoxyribonucleic acid (DNA) molecule in a bathing solution, where we concurrently couple atomistic bundled water and ions with the coarse-grained MARTINI model of the solvent. We use our fine-grained salt solution model as a solvent in the inner shell surrounding the DNA molecule, whereas the solvent in the outer shell is modeled by the coarse-grained model. The solvent entities can exchange between the two domains and adapt their resolution accordingly. We critically asses the performance of our multiscale model in adaptive resolution simulations of an infinitely long DNA molecule, focusing on the structural characteristics of the solvent around DNA. Our analysis shows that the adaptive resolution scheme does not produce any noticeable artifacts in comparison to a reference system simulated in full detail. The effect of using a bundled-SPC model, required for multiscaling, compared to the standard free SPC model is also evaluated. Our multiscale approach opens the way for large scale applications of DNA and other biomolecules which require a large solvent reservoir to avoid boundary effects.

## Jurij Sablic, Matej Praprotnik, Rafael Delgado-Buscalioni Open boundary molecular dynamics of sheared star-polymer melts Soft Matter 12, 2416-2439, 2016.

Abstract
Open boundary molecular dynamics (OBMD) simulations of a sheared star polymer melt under isothermal conditions are performed to study the rheology and molecular structure of the melt under a fixed normal load. Comparison is made with the standard molecular dynamics (MD) in periodic (closed) boxes at a fixed shear rate (using the SLLOD dynamics). The OBMD system exchanges mass and momentum with adjacent reservoirs (buffers) where the external pressure tensor is imposed. Insertion of molecules in the buffers is made feasible by implementing there a low resolution model (blob-molecules with soft effective interactions) and then using the adaptive resolution scheme (AdResS) to connect with the bulk MD. Straining with increasing shear stress induces melt expansion and a significantly different redistribution of pressure compared with the closed case. In the open sample, the shear viscosity is also a bit lowered but more stable against the viscous heating. At a given Weissenberg number, molecular deformations and material properties (recoverable shear strain and normal stress ratio) are found to be similar in both setups. We also study the modelling effect of normal and tangential friction between monomers implemented in a dissipative particle dynamics (DPD) thermostat. Interestingly, the tangential friction substantially enhances the elastic response of the melt due to a reduction of the kinetic stress viscous contribution.

2015

## Julija Zavadlav, Rudolf Podgornik, Matej PraprotnikAdaptive resolution simulation of a DNA molecule in salt solution J. Chem. Theory Comput. 11, 5035-5044, 2015.

Abstract
We present a multiscale simulation of a DNA molecule in 1 M NaCl salt solution environment, employing the adaptive resolution simulation approach that allows the solvent molecules, i.e., water and ions, to change their resolution from atomistic to coarse-grained and vice versa adaptively on-the-fly. The region of high resolution moves together with the DNA center-of-mass so that the DNA itself is always modeled at high resolution. We show that our multiscale simulations yield a stable DNA–solution system, with statistical properties similar to those produced by the conventional all-atom molecular dynamics simulation. Special attention is given to the collective properties, such as the dielectric constant, as they provide a sensitive quality measure of our multiscale approach.

## Rafael Delgado-Buscalioni, Jurij Sablic, Matej PraprotnikOpen boundary molecular dynamics Eur. Phys. J. Special Topics 224, 2331-2349, 2015.

Abstract
This contribution analyzes several strategies and combination of methodologies to perform molecular dynamic simulations in open systems. Here, the term open indicates that the total system has boundaries where transfer of mass, momentum and energy can take place. This formalism, which we call Open Boundary Molecular Dynamics (OBMD), can act as interface of different schemes, such as Adaptive Resolution Scheme (AdResS) and Hybrid continuum-particle dynamics to link atomistic, coarse-grained (CG) and continuum (Eulerian) fluid dynamics in the general framework of fluctuating Navier-Stokes equations. The core domain of the simulation box is solved using all-atom descriptions. The CG layer introduced using AdResS is located at the outer part of the open box to make feasible the insertion of large molecules into the system. Communications between the molecular system and the outer world are carried out in the outer layers, called buffers. These coupling preserve momentum and mass conservation laws and can thus be linked with Eulerian hydro- dynamic solvers. In its simpler form, OBMD allows, however, to impose a local pressure tensor and a heat flux across the system’s boundaries. For a one component molecular system, the external normal pressure and temperature determine the external chemical potential and thus the independent parameters of a grand-canonical ensemble simulation. Extended ensembles under non-equilibrium stationary states can also be simulated as well as time dependent forcings (e.g. oscillatory rheology). To illustrate the robustness of the combined OBMD-AdResS method, we present simulations of star-polymer melts at equilibrium and in sheared flow.

## Rafael Delgado-Buscalioni, Jurij Sablic, Matej PraprotnikReply to comments by R. Klein on "Open boundary molecular dynamics" Eur. Phys. J. Special Topics 224, 2511-2513, 2015.

Abstract
We agree with prof. Klein [1] that there are some similarities between our method [2] and the one presented in Ref. [3] (see also Ref. [4]). There are, however, several relevant differences we would like to outline.

## Aleksandar Popadic, Matej Praprotnik, Petros Koumoutsakos, Jens H. WaltherContinuum simulations of water flow past fullerene molecules Eur. Phys. J. Special Topics 224, 2321-2330, 2015.

Abstract
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently by continuum flow solvers, allowing for investigations into spatiotemporal scales inaccessible to atomistic simulations.

## Julija Zavadlav, Manuel N. Melo, Siewert J. Marrink, Matej PraprotnikAdaptive resolution simulation of polarizable supramolecular coarse-grained water models J. Chem. Phys. 142, 244118, 2015.

Abstract
Multiscale simulations methods, such as adaptive resolution scheme, are becoming increasingly popular due to their significant computational advantages with respect to conventional atomistic simulations. For these kind of simulations, it is essential to develop accurate multiscale water models that can be used to solvate biophysical systems of interest. Recently, a 4-to-1 mapping was used to couple the bundled-simple point charge water with the MARTINI model. Here, we extend the supramolecular mapping to coarse-grained models with explicit charges. In particular, the two tested models are the polarizable water and big multiple water models associated with the MARTINI force field. As corresponding coarse-grained representations consist of several interaction sites, we couple orientational degrees of freedom of the atomistic and coarse-grained representations via a harmonic energy penalty term. This additional energy term aligns the dipole moments of both representations. We test this coupling by studying the system under applied static external electric field. We show that our approach leads to the correct reproduction of the relevant structural and dynamical properties.

## Stas Bevc, Christoph Junghans, Matej PraprotnikSTOCK: Structure mapper and online coarse-graining kit for molecular simulations J. Comput. Chem. 36, 467-477, 2015.

Abstract
We present a web toolkit STructure mapper and Online Coarse-graining Kit for setting up coarse-grained molecular simulations. The kit consists of two tools: structure mapping and Boltzmann inversion tools. The aim of the first tool is to define a molecular mapping from high, for example, all-atom, to low, that is, coarse-grained, resolution. Using a graphical user interface it generates input files, which are compatible with standard coarse-graining packages, for example, Versatile Object-oriented Toolkit for Coarse-graining Applications and DL_CGMAP. Our second tool generates effective potentials for coarse-grained simulations preserving the structural properties, for example, radial distribution functions, of the underlying higher resolution model. The required distribution functions can be provided by any simulation package. Simulations are performed on a local machine and only the distributions are uploaded to the server. The applicability of the toolkit is validated by mapping atomistic pentane and polyalanine molecules to a coarse-grained representation. Effective potentials are derived for systems of TIP3P (transferable intermolecular potential 3 point) water molecules and salt solution. The presented coarse-graining web toolkit is available at http://stock.cmm.ki.si.

2014

## Aleksandar Popadic, Jens H. Walther, Petros Koumoutsakos, Matej PraprotnikContinuum simulations of water flow in carbon nanotube membranes New J. Phys. 16, 082001, 2014.

Abstract
We propose the use of the Navier–Stokes equations subject to partial-slip boundary conditions to simulate water flows in Carbon NanoTube (CNT) membranes. The finite volume discretizations of the Navier–Stokes equations are combined with slip lengths extracted from molecular dynamics (MD) simulations to predict the pressure losses at the CNT entrance as well as the enhancement of the flow rate in the CNT. The flow quantities calculated from the present hybrid approach are in excellent agreement with pure MD results while they are obtained at a fraction of the computational cost. The method enables simulations of system sizes and times well beyond the present capabilities of MD simulations. Our simulations provide an asymptotic flow rate enhancement and indicate that the pressure losses at the CNT ends can be reduced by reducing their curvature. More importantly, our results suggest that flows at nanoscale channels can be described by continuum solvers with proper boundary conditions that reflect the molecular interactions of the liquid with the walls of the nanochannel.

## Julija Zavadlav, Manuel N. Melo, Ana V. Cunha, Alex H. de Vries, Siewert J. Marrink, Matej PraprotnikAdaptive resolution simulation of MARTINI solvents J. Chem. Theory Comput. 10, 2591-2598, 2014.

Abstract
We present adaptive resolution molecular dynamics simulations of aqueous and apolar solvents using coarse-grained molecular models that are compatible with the MARTINI force field. As representatives of both classes of solvents we have chosen liquid water and butane, respectively, at ambient temperature. The solvent molecules change their resolution back and forth between the atomistic and coarse-grained representations according to their positions in the system. The difficulties that arise from coupling to a coarse-grained model with a multimolecule mapping, for example, 4-to-1 mapping in the case of the Simple Point Charge (SPC) and MARTINI water models, could be successfully circumvented by using bundled water models. We demonstrate that the presented multiscale approach faithfully reproduces the structural and dynamical properties computed by reference fully atomistic molecular dynamics simulations. Our approach is general and can be used with any atomistic force field to be linked with the MARTINI force field.

## Julija Zavadlav, Manuel N. Melo, Siewert J. Marrink, Matej PraprotnikAdaptive resolution simulation of an atomistic protein in MARTINI water J. Chem. Phys. 140, 054114, 2014.

Abstract
We present an adaptive resolution simulation of protein G in multiscale water. We couple atomistic water around the protein with mesoscopic water, where four water molecules are represented with one coarse-grained bead, farther away. We circumvent the difficulties that arise from coupling to the coarse-grained model via a 4-to-1 molecule coarse-grain mapping by using bundled water models, i.e., we restrict the relative movement of water molecules that are mapped to the same coarse-grained bead employing harmonic springs. The water molecules change their resolution from four molecules to one coarse-grained particle and vice versa adaptively on-the-fly. Having performed 15 ns long molecular dynamics simulations, we observe within our error bars no differences between structural (e.g., root-mean-squared deviation and fluctuations of backbone atoms, radius of gyration, the stability of native contacts and secondary structure, and the solvent accessible surface area) and dynamical properties of the protein in the adaptive resolution approach compared to the fully atomistically solvated model. Our multiscale model is compatible with the widely used MARTINI force field and will therefore significantly enhance the scope of biomolecular simulations.

2013

## Stas Bevc, Christoph Junghans, Kurt Kremer, Matej PraprotnikAdaptive resolution simulation of salt solutions New J. Phys. 15, 105007, 2013.

Abstract
We present an adaptive resolution simulation of aqueous salt (NaCl) solutions at ambient conditions using the adaptive resolution scheme. Our multiscale approach concurrently couples the atomistic and coarse-grained models of the aqueous NaCl, where water molecules and ions change their resolution while moving from one resolution domain to the other. We employ standard extended simple point charge (SPC/E) and simple point charge (SPC) water models in combination with AMBER and GROMOS force fields for ion interactions in the atomistic domain. Electrostatics in our model are described by the generalized reaction field method. The effective interactions for water–water and water–ion interactions in the coarse-grained model are derived using structure-based coarse-graining approach while the Coulomb interactions between ions are appropriately screened. To ensure an even distribution of water molecules and ions across the simulation box we employ thermodynamic forces. We demonstrate that the equilibrium structural, e.g. radial distribution functions and density distributions of all the species, and dynamical properties are correctly reproduced by our adaptive resolution method. Our multiscale approach, which is general and can be used for any classical non-polarizable force-field and/or types of ions, will significantly speed up biomolecular simulation involving aqueous salt.

2012

## Jens H. Walther, Matej Praprotnik, Evangelos M. Kotsalis, Petros KoumoutsakosMultiscale simulation of water flow past a C540 fullerene J. Comput. Phys. 231, 2677-2681, 2012.

Abstract
We present a novel, three-dimensional, multiscale algorithm for simulations of water flow past a fullerene. We employ the Schwarz alternating overlapping domain method to couple molecular dynamics (MD) of liquid water around the C540 buckyball with a Lattice–Boltzmann (LB) description for the Navier–Stokes equations. The proposed method links the MD and LB domains using a fully three-dimensional interface and coupling of velocity gradients. The present overlapping domain method implicitly preserves the flux of mass and momentum and bridges flux-based and Schwarz domain decomposition algorithms. We use this method to determine the slip length and hydrodynamic radius for water flow past a buckyball.

2011

## Matej Praprotnik, Simon Poblete, Kurt KremerStatistical physics problems in adaptive resolution computer simulations of complex fluids J. Stat. Phys. 145, 946-966, 2011.

Abstract
Simulating complex fluids or in general complex molecular systems requires approaches covering decades of time and length scales. This usually cannot be achieved within one simulation model. Over the years many different methods and models have been developed ranging from rather generic models, representing most efficiently the universal statistical mechanical properties of e.g. polymers, to all atom models and even quantum mechanical treatments. While these allow for scientifically very important studies in their own right, only a combination and close link between models of different levels allows for a truly quantitative description of materials and processes. In the present contribution we discuss an adaptive resolution approach where different levels of detail are treated within one simulation and the molecules are free to diffuse between different regions in space, where the molecules interact with different interaction potentials.

## Matej Praprotnik, Simon Poblete, Luigi Delle Site, Kurt KremerComment on "Adaptive multiscale molecular dynamics of macromolecular fluids" Phys. Rev. Lett. 107, 099801, 2011.

Abstract
A Comment on the Letter by S. O. Nielsen, P. B. Moore, and B. Ensing, Phys. Rev. Lett. 105, 237802 (2010). The authors of the Letter offer a Reply.

## Stas Bevc, Janez Konc, Jure Stojan, Milan Hodoscek, Matej Penca, Matej Praprotnik, Dusanka JanezicENZO: a web tool for derivation and evaluation of kinetic models of enzyme catalyzed reactions" PLoS ONE 6, e22265, 2011.

Abstract
We describe a web tool ENZO (Enzyme Kinetics), a graphical interface for building kinetic models of enzyme catalyzed reactions. ENZO automatically generates the corresponding differential equations from a stipulated enzyme reaction scheme. These differential equations are processed by a numerical solver and a regression algorithm which fits the coefficients of differential equations to experimentally observed time course curves. ENZO allows rapid evaluation of rival reaction schemes and can be used for routine tests in enzyme kinetics. It is freely available as a web tool, at http://enzo.cmm.ki.si.

2010

## Simon Poblete, Matej Praprotnik, Kurt Kremer, Luigi Delle SiteCoupling different levels of resolution in molecular simulations J. Chem. Phys. 132, 114101, 2010.

Abstract
Simulation schemes for liquids or strongly fluctuating systems that allow to change the molecular representation in a subvolume of the simulation box while preserving the equilibrium with the surroundings introduce conceptual problems of thermodynamic consistency. In this work we present a general scheme based on thermodynamic arguments which ensures a thermodynamic equilibrium among molecules of different representations. The robustness of the algorithm is tested for two examples, namely, an adaptive resolution simulation, atomistic/coarse grained, for a liquid of tetrahedral molecules, and an adaptive resolution simulation of a binary mixture of tetrahedral molecules and spherical solutes.

2009

## Rafael Delgado-Buscalioni, Kurt Kremer, Matej PraprotnikCoupling atomistic and continuum hydrodynamics through a mesoscopic model: Application to liquid water J. Chem. Phys. 131, 244107, 2009.

Abstract
We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under nonequilibrium conditions.

## Matej Praprotnik, Silvina Matysiak, Luigi Delle Site, Kurt Kremer, Cecilia ClementiCorrigendum: Adaptive resolution simulation of liquid water J. Phys.: Condens. Matter 21, 499801, 2009.

Abstract
In our two papers [1, 2] , we used a rigid all-atom TIP3P water model with a H-O-H angle of 112.20° instead of, as erroneously stated, the standard rigid TIP3P model [3] with a 104.52° H-O-H angle. All the other parameters are the same as in the standard rigid TIP3P water model. The statistical properties of similarly modified water models have been studied by other authors, cf references [4–6] . Since in the adaptive resolution simulations reported in references [1, 2] the modified TIP3P all-atom water model was studied in combination with the appropriate coarse-grained model, all conclusions of the paper concerning the adaptive resolution simulation remain unaltered.

2008

## Rafael Delgado-Buscalioni, Kurt Kremer, Matej PraprotnikConcurrent triple-scale simulation of molecular liquids J. Chem. Phys. 128, 114110, 2008.

Abstract
We present a triple-scale simulation of a molecular liquid, in which the atomistic, coarse-grained, and continuum descriptions of the liquid are concurrently coupled. The presented multiscale approach, which covers the length scales ranging from the micro- to macroscale, is a combination of two dual-scale models: a particle-based adaptive resolution scheme (AdResS), which couples the atomic and mesoscopic scales, and a hybrid continuum-molecular dynamics scheme (HybridMD). The combined AdResS-HybridMD scheme successfully sorts out the problem of large molecule insertion in the hybrid particle-continuum simulations of molecular liquids. The combined model is shown to correctly describe the hydrodynamics within a hybrid particle-continuum framework. The presented approach opens up the possibility to perform efficient grand-canonical molecular dynamics simulations of truly open molecular liquid systems.

## Matej Praprotnik, Luigi Delle Site, Kurt KremerMultiscale simulation of soft matter: From scale bridging to adaptive resolution Annu. Rev. Phys. Chem. 59, 545-571, 2008.

Abstract
The relation between atomistic chemical structure, molecular architecture, molecular weight, and material properties is of basic concern in modern soft material science and includes standard properties of bulk materials and surface and interface aspects, as well as the relation between structure and function in nanoscopic objects and molecular assemblies of both synthetic and biological origin. This all implies a thorough understanding on many length and correspondingly time scales, ranging from (sub)atomistic to macroscopic. Presently, computer simulations play an increasingly important, if not central, role. Some problems do not require specific atomistic details, whereas others require them only locally. However, in many cases this strict separation is not sufficient for a comprehensive understanding of systems, and flexible simulation schemes are required that link the different levels of resolution. We here give a general view of the problem regarding soft matter and discuss some specific examples of linked simulation techniques at different resolution levels. We then discuss a recently developed flexible simulation scheme, the AdResS method, which allows one to adaptively change the resolution in certain regions of space on demand.

## Matej Praprotnik, Christoph Junghans, Luigi Delle Site, Kurt KremerSimulation approaches to soft matter: Generic statistical properties vs. chemical details Comput. Phys. Commun. 179, 51-60, 2008.

Abstract
The relation between atomistic structure, architecture, molecular weight and material properties is a basic concern of modern soft material science. This by now goes far beyond standard properties of bulk materials. A typical additional focus is on surface or interface aspects or on the relation between structure and function in nanoscopic molecular assemblies. This all implies a thorough understanding on many length and correspondingly time scales ranging from (sub-)atomic to macroscopic. At this point computer simulations are playing an increasingly important, if not the central role. Traditionally simulations have been separated in two main groups, namely simplified models to deal with generic or universal aspects of polymers, i.e. critical exponents, and those employing classical force field simulations with (almost) all atomistic detail, i.e. for the diffusion of small additives in a small “sample”. Still characteristic problems, which require huge systems and/or long times in combination with a chemistry specific model, cannot be tackled by these methods alone. More recently with the development of scale bridging or multiscale simulation techniques, these different approaches have been combined into an emerging rather powerful tool. It is the purpose of this contribution to give a few examples of how such an approach can be used to understand specific material properties.

## Silvina Matysiak, Cecilia Clementi, Matej Praprotnik, Kurt Kremer, Luigi Delle SiteModeling diffusive dynamics in adaptive resolution simulation of liquid water J. Chem. Phys. 128, 024503, 2008.

Abstract
We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a coarse-grained to an all-atom representation and vice versa on-the-fly. In order to find the most appropriate coarse-grained watermodel to be employed with AdResS, we first study the accuracy of different coarse-grained watermodels in reproducing the structural properties of the all-atom system. Typically, coarse-grained molecular models have a higher diffusion constant than the corresponding all-atom models due to the reduction in degrees of freedom (DOFs) upon coarse-graining that eliminates the fluctuating forces associated with those integrated-out molecular DOFs. Here, we introduce the methodology to obtain the same diffusionaldynamics across different resolutions. We show that this approach leads to the correct description of the here relevant structural, thermodynamical, and dynamical properties, i.e., radial distribution functions, pressure, temperature, and diffusion, of liquid water at ambient conditions.

## Christoph Junghans, Matej Praprotnik, Kurt KremerTransport properties controlled by a thermostat: An extended dissipative particle dynamics thermostat Soft Matter 4, 156-161, 2008.

Abstract
We introduce a variation of the dissipative particle dynamics (DPD) thermostat that allows for controlling transport properties of molecular fluids. The standard DPD thermostat acts only on a relative velocity along the interatomic axis. Our extension includes the damping of the perpendicular components of the relative velocity, whilst keeping the advantages of conserving Galilei invariance and within our error bar also hydrodynamics. This leads to a second friction parameter for tuning the transport properties of the system. Numerical simulations of a simple Lennard-Jones fluid and liquid water demonstrate a very sensitive behaviour of the transport properties, e.g., viscosity, on the strength of the new friction parameter. We envisage that the new thermostat will be very useful for the coarse-grained and adaptive resolution simulations of soft matter, where the diffusion constants and viscosities of the coarse-grained models are typically too high/low, respectively, compared to all-atom simulations.

## Matej Praprotnik, Stanko Hocevar, Milan Hodoscek, Matej Penca, Dusanka JanezicNew all-atom force field for molecular dynamics simulation of AlPO4-34 molecular sieve J. Comput. Chem. 29, 122-129, 2008.

Abstract
A force field of the triclinic framework of AlPO4-34, important in methanol–hydrocarbon conversion reactions, was developed using an empirical potential function. Molecular dynamics simulation of an AlPO4-34 triclinic framework segment of 1216 atoms, containing the template molecules isopropylamine and water, was performed with explicit consideration of atomic charges. The average RMS difference between instantaneous positions of the framework atoms during 1 ns simulation and their positions in the structure determined from single crystal X-ray diffraction was calculated, and the average structure of the flexible framework was determined. The computed Debye-Waller factors and simulated FTIR spectra are in good agreement with the experimental data. The new force field permits detailed molecular dynamics simulations of flexible, charged aluminophosphate molecular sieves which should lead to a better understanding of the catalytic processes and the crucial role played by templating molecules.

2007

## Matej Praprotnik, Silvina Matysiak, Luigi Delle Site, Kurt Kremer, Cecilia ClementiAdaptive resolution simulation of liquid water J. Phys.: Condens. Matter 19, 292201, 2007.

Abstract
Water plays a central role in biological systems and processes, and is equally relevant in a large range of industrial and technological applications. Being the most important natural solvent, its presence uniquely influences biological function as well as technical processes. Because of their importance, aqueous solutions are among the most experimentally and theoretically studied systems. However, many questions still remain open. Both experiments and theoretical models are usually restricted to specific cases. In particular all-atom simulations of biomolecules and materials in water are computationally very expensive and often not possible, mainly due to the computational effort to obtain water–water interactions in regions not relevant for the problem under consideration. In this paper we present a coarse-grained model that can reproduce the behaviour of liquid water at a standard temperature and pressure remarkably well. The model is then used in a multiscale simulation of liquid water, where a spatially adaptive molecular resolution procedure allows one to change from a coarse-grained to an all-atom representation on-the-fly. We show that this approach leads to the correct description of essential thermodynamic and structural properties of liquid water. Our adaptive multiscale scheme allows for significantly greater extensive simulations than existing approaches by taking explicit water into account only in the regions where the atomistic details are physically relevant.

## Matej Praprotnik, Luigi Delle Site, Kurt KremerA macromolecule in a solvent: Adaptive resolution molecular dynamics simulation J. Chem. Phys. 126, 134902, 2007.

Abstract
The authors report adaptive resolution molecular dynamics simulations of a flexible linear polymer in solution. The solvent, i.e., a liquid of tetrahedral molecules, is represented within a certain radius from the polymer’s center of mass with a high level of detail, while a lower coarse-grained resolution is used for the more distant solvent. The high resolution sphere moves with the polymer and freely exchanges molecules with the low resolution region through a transition regime. The solvent molecules change their resolution and number of degrees of freedom on the fly. The authors show that their approach correctly reproduces the static and dynamic properties of the polymer chain and surrounding solvent.

## Matej Praprotnik, Kurt Kremer, Luigi Delle SiteFractional dimensions of phase space variables: a tool for varying the degrees of freedom of a system in a multiscale treatment   J. Phys. A: Math. Theor. 40, F281-F288, 2007.

Abstract
We show how the idea of fractal dimensions of phase space variables can be employed to develop a concept of adaptive resolution treatment of a molecular liquid. The resulting theoretical framework allows for calculation of statistical averages of thermodynamic quantities in multiresolution computer simulation algorithms where the molecular degrees of freedom change on the fly.

## Matej Praprotnik, Kurt Kremer, Luigi Delle SiteAdaptive molecular resolution via a continous change of the phase space dimensionality Phys. Rev. E 75, 017701, 2007.

Abstract
For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or by far too small time scales. To overcome this problem multiscale techniques are being developed. However, in almost all cases, the regions and molecules of different resolution are kept fixed and are not in equilibrium with each other. We here give a basic theoretical framework for an efficient and flexible coupling of the different regimes. The approach leads to a concept, which can be seen as a geometry-induced phase transition, and to a counterpart of the equipartition theorem for fractional degrees of freedom. This represents the initial step in developing a general theoretical framework for computer simulation methods applying simultaneously different levels of resolution.

2006

## Matej Praprotnik, Luigi Delle Site, Kurt KremerAdaptive resolution scheme for efficient hybrid atomistic-mesoscale molecular dynamics simulations of dense liquids   Phys. Rev. E 73, 066701, 2006.

Abstract
The adaptive resolution scheme (AdResS) for efficient hybrid particle-based atomistic/mesoscale molecular dynamics (MD) simulations recently introduced by us, [J. Chem. Phys. 123, 224106 (2005)] is extended to high density molecular liquids with spherical boundaries between the atomistic and mesoscale regions. The key feature of this approach is that it allows for a dynamical change of the number of molecular degrees of freedom during the course of a MD simulation by an on-the-fly switching between the atomistic and mesoscopic levels of detail. Pressure and density variations occurring at the atomistic/mesoscale boundary in the original version are considerably reduced employing the improved methodology presented here.

2005

## Matej Praprotnik, Luigi Delle Site, Kurt KremerAdaptive resolution molecular-dynamics simulation: Changing the degrees of freedom on the fly J. Chem. Phys. 123, 224106, 2005.

Abstract
We present a new adaptive resolution technique for efficient particle-based multiscale molecular-dynamics simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecule’s atomic and coarse-grained levels of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a modelsystem of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, and the other containing only one-particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The hybrid and the atomistically resolved systems have the same statistical properties at the same physical conditions.

## Matej Praprotnik, Dusanka JanezicMolecular dynamics integration meets standard theory of molecular vibrations J. Chem. Inf. Model. 45, 1571-1579, 2005.

Abstract
An iterative SISM (split integration symplectic method) for molecular dynamics (MD) integration is described. This work explores an alternative for the internal coordinate system prediction in the SISM introduced by Janežič et al. (J. Chem. Phys. 2005, 122, 174101). The SISM, which employes a standard theory of molecular vibrations, analytically resolves the internal high-frequency molecular vibrations. This is accomplished by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The Eckart frame, which is usually used in the standard theory of molecular vibrations as an internal coordinate system of a molecule, is adopted to be used within the framework of the second order generalized leapfrog scheme. In the presented MD integrator the internal coordinate frame at the end of the integration step is predicted halfway through the integration step using a predictor-corrector type iterative approach thus ensuring the method's time reversibility. The iterative SISM, which is applicable to any system of molecules with one equilibrium configuration, was applied here to perform all-atom MD simulations of liquid CO2 and SO2. The simulation results indicate that for the same level of accuracy, this algorithm allows significantly longer integration time steps than the standard second-order leapfrog Verlet (LFV) method.

## Dusanka Janezic, Matej Praprotnik, Franci MerzelMolecular dynamics integration and molecular vibrational theory. I. New symplectic integrators J. Chem. Phys. 122, 174101, 2005.

Abstract
New symplectic integrators have been developed by combining molecular dynamics integration with the standard theory of molecular vibrations to solve the Hamiltonian equations of motion. The presented integrators analytically resolve the internal high-frequency molecular vibrations by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The translation and rotation of a molecule are treated as vibrational motions with the vibrational frequency zero. All types of motion are thus described in terms of the normal coordinates. The method’s time reversibility requirement was used to determine the equations of motion for internal coordinate system of a molecule. The calculation of long-range forces is performed numerically within the generalized second-order leap-frog scheme, in the same way as in standard second-order symplectic methods. The new methods for integrating classical equations of motion using normal modeanalysis allow us to use a long integration step and are applicable to any system of molecules with one equilibrium configuration.

## Matej Praprotnik, Dusanka JanezicMolecular dynamics integration and molecular vibrational theory. II. Simulation of nonlinear molecules J. Chem. Phys. 122, 174102, 2005.

Abstract
A series of molecular dynamics (MD) simulations of nonlinear molecules has been performed to test the efficiency of newly introduced semianalytical second-order symplectic time-reversible MD integrators that combine MD and the standard theory of molecular vibrations. The simulation results indicate that for the same level of accuracy, the new algorithms allow significantly longer integration time steps than the standard second-order symplectic leap-frog Verlet method. Since the computation cost per integration step using new MD integrators with longer time steps is approximately the same as for the standard method, a significant speed-up in MD simulation is achieved.

## Matej Praprotnik, Dusanka JanezicMolecular dynamics integration and molecular vibrational theory. III. The infrared spectrum of water J. Chem. Phys. 122, 174103, 2005.

Abstract
The new symplectic molecular dynamics (MD) integrators presented in the first paper of this series were applied to perform MD simulations of water. The physical properties of a system of flexible TIP3P water molecules computed by the new integrators, such as diffusion coefficients, orientation correlation times, and infrared (IR) spectra, are in good agreement with results obtained by the standard method. The comparison between the new integrators’ and the standard method’s integration time step sizes indicates that the resulting algorithm allows a 3.0fs long integration time step as opposed to the standard leap-frog Verlet method, a sixfold simulation speed-up. The accuracy of the method was confirmed, in particular, by computing the IR spectrum of water in which no blueshifting of the stretching normal mode frequencies is observed as occurs with the standard method.

2004

## Matej Praprotnik, Dusanka Janezic, Janez MavriTemperature dependence of water vibrational spectrum: A molecular dynamics simulation study J. Phys. Chem. A 108, 11056-11062, 2004.

Abstract
Vibrational spectroscopy studies show that the bulk water bending band becomes narrower with increasing temperature (Maréchal, Y. J. Mol. Struct. 1994, 322, 105). Since this counterintuitive effect is not associated with the quantum nature of nuclear motion a molecular dynamics (MD) simulation is expected to reproduce it even in the classical limit. We have performed a classical MD simulation of the flexible simple point charge (SPC) and extended SPC (SPC/E) water models to determine the temperature dependence of the bulk water vibrational spectrum. The intramolecular water potential proposed by Toukan and Rahman, including a stretch−bend coupling term, was applied. We performed MD simulations at −4 and 80 °C to compare the calculated vibrational spectra, in particular, the band associated with the bending mode, with the experiment. The experimentally determined narrowing of the bending band with increasing temperature is not reproducible by MD simulation with the applied force field. However, the results show that this approach successfully reproduces all other experimentally observed spectroscopic properties of bulk water.

## Roman Trobec, Marjan Sterk, Matej Praprotnik, Dusanka JanezicParallel programming library for molecular dynamics simulations Int. J. Quant. Chem. 96, 530-536, 2004.

Abstract
A parallel programming library for molecular dynamics (MD) simulations is described and applied to the recently proposed split integration symplectic method (SISM) for MD simulation. The results show that for a system of 1024 linear chain molecules with an integration step of 4.5 fs parallel execution of SISM with the particle–particle interactions (PPIs) library on 32 computers gives efficiency of 95.6%. The results also show the parallel simulation of n particles is scalable with the number of processors p and the time requirement is proportional to n2/p for n/p large enough, which guarantees optimal speed-up.

## Matej Praprotnik, Marjan Sterk, Roman TrobecInhomogeneous heat-conduction problems solved by a new explicit finite difference scheme IJPAM 13, 275-291, 2004.

Abstract
A heat conduction in systems composed of biomaterials, such as the heart muscle, is described by the familiar heat conduction equation. Due to the inhomogeneity of these materials the equations defining the diffusion problem are difficult to solve. A new explicit finite difference scheme for solving the heat conduction equation for inhomogeneous materials is derived. The new scheme has the same computational complexity as the standard scheme and gives the same solution but with increased resolution of the temperature grid. It was derived and studied on a simple one dimensional problem of heat conduction and applied to studying the temperature distribution in a three dimensional model of the heart muscle.

2003

## Dusanka Janezic, Matej PraprotnikMolecular dynamics integration time step dependence of the split integration symplectic method on system density J. Chem. Inf. Comput. Sci. 43, 1922-1927, 2003.

Abstract
This paper shows that the maximal size of the integration time step of the Split Integration Symplectic Method (SISM) for molecular dynamics (MD) integration, a combination of the analytical solution of the high-frequency harmonic part of the Hamiltonian and the numerical solution of the low-frequency remaining part, depends on the system density. This approach was tested on a system of linear chain molecules. The numerical results indicate that the integration time step used by the SISM is limited by atoms' motion generated by the electrostatic and Lennard-Jones interactions in the system. As the density of the system increases, the size of the integration time step allowed by the SISM thus becomes smaller but remains significantly larger than possible by standard methods of the same order and complexity.

2002

## Marjan Sterk, Roman Trobec, Matej PraprotnikNumerical schemes for fluid flow and heat transfer in medical simulations Parallel and Distributed Computing Practices 5, 321-329, 2002.

Abstract
Incompressible fluid flow is governed by the Navier-Stokes equation, which, together with the diffusion and continuity equations, forms a coupled system of partial differential equations that have to be solved to simulate the fluid dynamics. We describe a finite difference scheme and boundary conditions used to solve the system of partial differential equations on general 3-dimensional domains with explicit integration in time. The most computationally intensive part is the pressure equation that requires the solution of a sparse linear system in each time-step of the simulation. Various iterative methods for the solution of the linear system are tested and compared among which the multigrid method outperforms others. Some test examples are given to prove the validity of the simulation results. The paper concludes with an analysis of parallel computational complexity of the SOR method and parallelization strategy for the multigrid method.

## Matej Praprotnik, Dusanka JanezicThe Split Integration Symplectic Method Cell. Mol. Biol. Lett. 7, 147-148, 2002.

Abstract
The split integration symplectic method (SISM) for Hamiltonian systems based on factorization of the Liouvillepropagator is presented.

2001

## Roman Trobec, Marjan Sterk, Matej Praprotnik, Dusanka JanezicImplementation and evaluation of MPI-based parallel MD program Int. J. Quant. Chem. 84, 23-31, 2001.

Abstract
The message-passing interface (MPI)-based object-oriented particle–particle interactions (PPI) library is implemented and evaluated. The library can be used in the n-particle simulation algorithm designed for a ring of p interconnected processors. The parallel simulation is scalable with the number of processors, and has the time requirement proportional to n2/p if n/p is large enough, which guarantees optimal speedup. In a certain range of problem sizes, the speedup becomes superlinear because enough cache memory is available in the system. The library is used in a simple way by any potential user, even with no deep programming knowledge. Different simulations using particles can be implemented on a wide spectrum of different computer platforms. The main purpose of this article is to test the PPI library on well-known methods, e.g., the parallel molecular dynamics (MD) simulation of the monoatomic system by the second-order leapfrog Verlet algorithm. The performances of the parallel simulation program implemented with the proposed library are competitive with a custom-designed simulation code. Also, the implementation of the split integration symplectic method, based on the analytical calculation of the harmonic part of the particle interactions, is shown, and its expected performances are predicted.

## Dusanka Janezic, Matej PraprotnikSymplectic molecular dynamics integration using normal mode analysis Int. J. Quant. Chem. 84, 2-12, 2001.

Abstract
The split integration symplectic method (SISM) for molecular dynamics (MD) integration using normal mode analysis based on a factorization of the Liouville propagator is presented. This approach is quite distinct from others that use fractional-step methods, owing to the analytical treatment of high-frequency motions. The method involves splitting the total Hamiltonian of the system into a harmonic part and the remaining part. Then the Hamilton equations are solved using a second-order generalized leapfrog integration scheme in which the purely harmonic Hamiltonian (which represents the main contribution of the chemical bonds and angles) is treated analytically, i.e., independent of the step size of integration, by a normal mode analysis that is carried out only once, at the beginning of calculation. The whole integration step combines analytical evolution of the harmonic part of the Hamiltonian with a correction arising from the remaining part. The proposed algorithm requires only one force evaluation per integration step. The algorithm was tested on a simple system of linear chain molecules. Results demonstrate the method makes possible the integration of the MD equations over larger time steps without loss of stability while being economical in computer time.

## Matej Praprotnik, Luigi Delle Site Multiscale molecular modeling Biomolecular Simulations: Methods and Protocols, Luca Monticelli, Emppu Salonen (Eds.), Methods in Molecular Biology, vol. 924, pp. 567-583, Springer Science+Business Media, New York, 2013.

Abstract
We review the basic theoretical principles of the adaptive resolution simulation scheme (AdResS). This method allows to change molecular resolution on-the-fly during a simulation by changing the number of degrees of freedom in specific regions of space where the required resolution is higher than in the rest of the system. We also report about recent extensions of the method to the continuum and quantum regimes.

## Dusanka Janezic, Urban Borstnik, Matej Praprotnik Parallel approaches in molecular dynamics simulations Parallel computing : Numerics, Applications, and Trends, R. Trobec, M. Vajtersic, P. Zinterhof (Eds.), pp. 281-305, Springer, Dordrecht, 2009.

Abstract
In this contribution we will present the survey of our past and current endeavor on parallel approaches in molecular modeling algorithm development, for example, molecular dynamics (MD) simulation. In particular, we will describe the new split integration symplectic method for the numerical solution of molecular dynamics equations and methods for the determination of vibrational frequencies and normal modes of large systems, and the distributed diagonal force decomposition method, a parallel method for MD simulation.

## Christoph Junghans, Matej Praprotnik, Luigi Delle Site Adaptive resolution schemes Multiscale simulation methods in molecular sciences, J. Grotendorst, N. Attig, S. Blügel, D. Marx (Eds.), NIC series, vol. 42, pp. 359-379, Institute for Advanced Simulation, Forschungszentrum Jülich, 2009.

Abstract
The Adaptive Resolution Scheme (AdResS) is a simulation method, which allows to perform Molecular Dynamics (MD) simulations treating different regions with different molecular resolutions. The different scales are coupled within a unified approach by changing the number of degrees of freedom on the fly and preserving the free exchange of particles between regions of different resolution. Here we describe the basic physical principles of the algorithm and illustrate some of its relevant applications.